Chapter 7 Deductive Reasoning Categorical Logic 4 Standard

Chapter 7 Deductive Reasoning: Categorical Logic

4 Standard Categorical Statements 1. All S are P. (All cats are carnivores. ) 2. No S are P. (No cats are carnivores. ) 3. Some S are P. (Some cats are carnivores. ) 4. Some S are not P. (Some cats are not carnivores. )

Quality and Quantity of the 4 Standard Categorical Statements: • A All S are P (universal affirmative) • E No S are P (universal negative) • I Some S are P (particular affirmative) • O Some S are not P (particular negative)

S P All S are P

S P No S are P

X S P Some S are P

X S P Some S are not P

Categorical Syllogism 1. Major Premise 1. [middle term] [major term]. 2. Minor Premise 2. [minor term] [middle term]. 3. Conclusion 3. Therefore, [minor term] [major term]. 1. All egomaniacs are warmongers. 2. All dictators are egomaniacs. 3. Therefore, all dictators are warmongers. 1. All M are P. 2. All S are M. 3. Therefore, all S are P.

The Square of Opposition

The Square of Opposition Contraries: • A- and E- statements Subcontraries: • I- and O-statements Contradictories: • A- and O-statements • E- and I-statements

Categorical Equivalence Conversion: Reverse the positions of the subject and predicate terms. Obversion: (1) Replace the predicate term with the term’s complement and (2) switch the statement from affirmative to negative, or negative to affirmative. Contraposition: (1) Reverse the positions of the subject and predicate terms and (2) substitute complement terms for the subject and predicate terms.